Welcome to the DIS!

We're glad you joined us. I have never stayed at a moderate (only value and deluxe), so I can't help with that choice. I have stayed at every deluxe except the Contemporary, so hopefully I can help with that.
My favorites are:
Grand Floridian (GF)
Animal Kingdom Lodge (AKL)
Yacht Club and BoardWalk Inn--tied for third (YC and BWI)
Of those three, the AKL is the least expensive, and it has rooms with bunkbeds, which the kids might enjoy. Plus, savannah view rooms have incredible views--it's really neat. It is a little remote though, so expect slightly long bus rides to get to the Magic Kingdom and Epcot.
The Grand Floridian is very elegant and feminine, which really appeals to me. Despite its elegance, kids are certainly welcome--it is Disney after all! It is also located on the monorail, so you would have very quick access to the Magic Kingdom and Epcot.
The Yacht Club and BoardWalk Inn are located right across a lagoon from each other, so their location is essentially the same. It's within walking distance of Epcot, and a longer walk to Disney-MGM Studios. Of course, that's very nice to be able to walk to some parks. The Yacht Club has a terrific pool area called Stormalong Bay, which the kids would love (it's heated year-round).
I would check out the pictures of the rooms on
www.wdwig.com and
www.ourlaughingplace.com to help you decide which theme appeals to you the most.
